can someone please help? the question is an equilateral triangle is sometimes/always/never similar to a scalene triangle, because we can sometimes/always/never map one onto the other using only dial actions rigid transformations.

Can Someone Please Help? The Question Is An Equilateral Triangle Is Sometimes/always/never Similar To

Answers

Answer 1

Answer:

An equilateral triangle is never similar to a scalene triangle, because we can never map one onto the other using only dilations and rigid transformations.

======================================================

Explanation:

An equilateral triangle is one where it has all three sides the same length. "Equi" means "equal" while "lateral" means "side". Any equilateral triangle also has all three angles the same measure (we consider it equiangular). Each angle is 60 degrees.

In contrast, a scalene triangle has all of its sides different, so consequently that means all of its three angles must be different as well. If you had exactly two angles congruent to one another, then the opposite sides would be a congruent pair of sides, but then that leads to an isosceles triangle. Also, if all three angles were the same, then we'd get back to an equilateral triangle. So in short, any scalene triangle has all of its angles different.

------------------

Let's consider two cases

Case 1) The scalene triangle has one angle that is 60 degrees, while the other two angles are not 60 degrees.Case 2) The scalene triangle doesn't have any angles that are 60 degrees.

If case 1 happens, then we could match up one pair of 60 degree corresponding angles between the equilateral triangle and the scalene triangle. However, we won't have any more matches. This is because the other two angles aren't 60 (if they were then the triangle isn't scalene). Therefore case 1 leads to dissimilar triangles.

If case 2 happens, then we get the same conclusion as case 1. This time we don't have any angles matching up. Similar triangles must have corresponding angles match up and be congruent. Put another way: similar triangles are the same shape but not necessarily the same size.

------------------

After completing both cases, we can see that it is impossible to have an equilateral triangle be similar to a scalene triangle. In terms of transformations, we cannot apply any of the following

TranslationReflectionRotationDilation

and have one triangle turn into the other. Again, it's all because the angles do not match up. We may have one matching pair, but we need all three pairs to match.


Related Questions

Simplify: 3(2x+7)-2(x+5)

Answers

Answer:

=4x+11

Step-by-step explanation:

Answer:

4x - 11

Step-by-step explanation:

3(2x+7)-2(x+5)

6x + 21 - 2x - 10

combine like terms

4x - 11

Hope this helps!!

The distance AB rounded to the nearest tenth = [ ? ]

Answers

Answer:

4.5 units

Step-by-step explanation:

To get the distance we need the coordinates of the points

A is ( 3,1)

B is (-1,-1)

Let A be (x1,y1) and B be (x2,y2)

So applying the formula, we have the distance as;

D = √(-1-3)^2 + (-1-1)^2

D = √(16 + 4)

D = √20

D = 4.5 units

What is a secure line of credit?
A)A line of credit offered only to individuals with excellent credit ratings.
B)A line of credit offered to a business or corporation.
C)A line of credit backed by the government.
D)A line of credit backed by collateral.

Answers

Answer:

It's D. A line of credit backed by collateral.

Step-by-step explanation:

Just took the test and got it right.

the secure line of credit is:

D)A line of credit backed by collateral.

What is Collateral?

Collateral is an item of value pledged to secure a loan. Collateral reduces the risk for lenders. If a borrower defaults on the loan, the lender can seize the collateral and sell it to recoup its losses. Mortgages and car loans are two types of collateralized loans.

A revolving loan that can be utilized for any purpose is known as a line of credit (LOC). Up to a maximum amount determined by the lender, the borrower may draw from the line of credit at any moment, pay it back, and then borrow again.

There are substantial variations between secured and unsecured lines of credit, including the interest rate that the borrower must pay.

Collateral, such as a house, serves as the guarantee for a secured line of credit.One example of an unsecured line of credit is a credit card, which is not backed by any assets.Because it is riskier for lenders, unsecured credit always has a higher interest rate.

Therefore, the secure line of credit is:

D)A line of credit backed by collateral.

Learn more about collateral here:

https://brainly.com/question/6779619

#SPJ6

Harry earned d dollars mowing lawns. He put 20% of his earnings in the bank and paid back $50.00 to his father. He spent one-fifth of the re mb ainig money on a video game. Which expreesion represents the amount he spent on the video game _,_,_,_

Answers

The question is incomplete.

Complete Question

Harry earned d dollars mowing lawns. He put 20% of his earnings in the bank and paid back $50.00 to his father. He spent one-fifth of the remaining money on a video game. Which expression represents the amount he spent on the video game?

(0.20 - 10) dollars

(0.20 - 50) dollars

(0.160 + 10) dollars

(0.160 - 10) dollars

Answer:

(0.160 - 10) dollars

Step-by-step explanation:

Let the total number of earnings be represented by d

Harry earned d dollars mowing lawns. He put 20% of his earnings in the bank

Amount in the bank = 20% of d = 0.20d

He paid back $50.00 to his father.

The amount left = 1d - 0.20d = 0.80d

He paid back his father

Hence:

= (d - 0.20d) - $50

= 0.80d -$50.00

He spent one-fifth of the remaining money on a video game.

The amount remaining

= 0.80d -$50.00

Hence, the amount he spent on video games =

1/5(0.80d - $50.00)

(0.16d - $10.00)

= (0.16d - 10)

= (0.16 - 10) dollars

-
What is the slope of the line Perpendicular to y = -x- 10
-4
04
o
o Zero
Need help

Answers

Answer:

A. -4

Step-by-step explanation:

Perpendicular lines have negative slopes

so you would have to flip the fraction and change the sign

so 1/4x = -4/1x or -4x

PROBLEM SOLVING The profit P (in millions of dollars) for a shoe manufacturer can be modeled by P= -21x3 + 46x where x
is the number (in millions) of shoes produced. The company now produces 1 million shoes and makes a profit of $25 million, but it
would like to cut back production. What lesser number of shoes could the company produce and still make the same profit?

Answers

Answer:

Step-by-step explanation:

at 700,200 shoes there is also a 25 million dollar profit

The city plans to extend the Wildflower Tral to make it 2 ½ times its current length in the next 5 years. How long will the Wildflower Trail be at the end of 5 years?

Answers

Answer: 5¹⁵/₁₆

Step-by-step explanation:

The Wildflower Trail is currently 2³/₈ miles long.

If the city will extend it by 2¹/₂ in 5 years, the length in five years will be;

= 2³/₈ * 2¹/₂

= 19/8 * 5/2

= 95/16

= 5¹⁵/₁₆

please can someone help me with this?

Answers

Point A is at (0,0). This is the origin.

To move to A'(5,2), we will do two things:

shift 5 units to the rightshift 2 units up

This will have (0,0) move to (5,2).

Points B,C, and D follow the same steps to get what the diagram shows. This is why the entire figure moves 5 units to the right and 2 units up. Everything is in lock-step with each other. This keeps the same shape and size.

If you want to use symbols, then you can describe the translation rule as [tex](x,y) \to (x+5, y+2)[/tex]. We add 5 to the x coordinate to shift 5 units to the right, and we add 2 to the y coordinate to shift 2 units up.

Allison can sew three scarves in 75 minutes how many scarves can she sew in 4 hours?

Answers

Answer: 9

Step-by-step explanation:

I think this is the answer based off a estimate

If the perimeter of a rectangle is 34 cm and the area is 60 square cm, then what are the dimensions of the
rectangle?

Answers

Answer: 12 by 12  by 5 by 5

Step-by-step explanation: 12*5 = 60

12+12+5+5

=34

Before Cam broke his right arm, he was able to type 9 words per minute on his phone. After he broke his arm, he had to use his left hand for a while, and he could only type 6 words per minute. What is the difference between the number of words he could type in 5 minutes before and after he broke his arm.

Answers

Answer:Before he broke his arm: 45 words in 5 minutes

After he broke his arm: 30 words in 5 minutes

9*5=45 6*5=30

Hope this helps... mark as Brainliest plz

Step-by-step explanation:

work out the input for this function machine ​

Answers

Answer:

Answer is 12 isnt it

Step-by-step explanation:

12×4=48

48+9=57

PLEASE HURRY

Which equation has only one solution?
O-5|=-1
O6-2x| =8
O 5x+ 10| =10
O-6x+ 3| = 0

Answers

Answer:

D

Step-by-step explanation:

|-6x+3|=0

-6x+3=0

-6x=-3

x=-3/-6

x=1/2

Solve the equation: [tex]5^x^(^x^-^1^)=1[/tex]

Answers

The concept:

We are given the equation:

[tex]5^{x(x-1)} = 1[/tex]

Which can be simplified as:

[tex]5^{x^{2} - x} = 1^{1}[/tex]

Since any number to the power '0' is 1

x² - x must be equal to 0 for the given equation to be true

Solving for x:

x² - x = 0

x(x-1) = 0

now, we can divide both sides by either x OR x-1

So we will see what we get for either choice:

x = 0/(x-1)                           x-1 = 0/x

x = 0                                  x = 1

Hence, the value of x is either 0 or 1


Is (3,4) a solution to the system of
equations.
X + y = 7
x - 2y = - 5

Answers

Answer: Yes, the point (3,4) is a solution to the system.

===================================================

Proof of this:

Replace x with 3 and y with 4 in the first equation

x+y = 7

3+4 = 7

7 = 7

This confirms the first equation. Repeat for the second equation

x-2y = -5

3-2(4) = -5

3 - 8 = -5

-5 = -5

We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).

Which ordered pair is a solution of the equation?
y = -6x+1

Answers

Answer:

2,-11

Step-by-step explanation:

create an x/y table and plug in #s for ordered pairs

-6x + 1 = y [plug in 2 for x]

-12 + 1 = -11 [ordered pair is 2, -11]

Answer:

Both (-2, 13) and (-1, 7)

Step-by-step explanation:

Got it from Khan

help is much appreciated!!

Find the value of T.

A. 12 B. 5 C. 4 D. 16

Answers

A because
The value
Of t
Is going
To be
12

A card is drawn from a
standard, well-shuffled
deck of 52 cards.
What is the probability that
it is a face card (J, Q, or K)?

Answers

12/52
3*4 = 12
there’s 52 cards in total

Aria borrowed some money from her friend in order to help buy a new video game
system. Aria agreed to pay the friend back some amount every week until her loan
was paid off. An equation representing the amount Aria owes her friend after t weeks
is L = -25t + 100. What is the x-intercept of the equation and what is its
interpretation in the context of the problem?

Answers

Answer:

t is the x-intercept

and it represents the weeks

Step-by-step explanation:

Answer: 4 is the x intercept for the number of weeks until loan is paid off

Step-by-step explanation:

Im supposed to solve this equation using logarithms but I don't know how.

Answers

Given:

[tex]3(4^x)=5^(x+1)[/tex]

To find:

The solution of the given equation.

Solution:

We have,

[tex]3(4^x)=5^(x+1)[/tex]

It can be written as

[tex]3((2^2)^x)=5^(x+1)[/tex]

[tex]3((2^{2x})=5^(x+1)[/tex]      [tex][\because (a^m)^n=a^{mn}][/tex]

Taking log on both sides.

[tex]\log [3((2^{2x})]=\log 5^(x+1)[/tex]

[tex]\log 3+ \log ((2^{2x})=\log 5^(x+1)[/tex]        [tex][\because \log (ab)=\log a+\log b][/tex]

[tex]\log 3+ 2x\log 2=(x+1)\log 5[/tex]      [tex][\because \log x^n=n\log x][/tex]

Putting values of logarithms, we get

[tex]0.477+ 2x(0.301)=(x+1)0.699[/tex]      [tex][\because \log 2 =0.301, \log 3=0.477, \log 5=0.699][/tex]

[tex]0.477+ 0.602x=0.699x+0.699[/tex]

[tex]0.602x-0.699x=0.699-0.477[/tex]

[tex]-0.097x=0.222[/tex]

Divide both sides by -0.097.

[tex]x=\dfrac{0.222}{-0.097}[/tex]

[tex]x=-2.288656[/tex]

[tex]x\approx -2.289[/tex]

Therefore, the value of x is -2.289.

Is it true that Terms with no variables are like terms?

Answers

Answer:

yes

Step-by-step explanation:

What is the solution to -(6 m + 8) = 4(17 - m)?

Answers

Answer:

m=-38

Step-by-step explanation:

The answer is m 38. hope this helps

DOES ANYONE KNOW THIS??

Answers

Answer:

49-9i²

Step-by-step explanation:

(7+3i)(7-3i)

expand the brackets

49-21i +21i -9i²

49-9i²

Please do it I don’t know how to

Answers

Answer:

Step-by-step explanation:

I'm that's hard to do

2) A big league pitching coach tries to limit his pitchers to 110
pitches per game. If the pitcher has already thrown 52
pitches, write and solve an inequality to find how many more
pitches he can throw before reaching the limit.

Answers

P is less than or equal to (<) 110-52 you want to use the < sign with a line under it. The minus 52 is because he has already thrown 52 out of his 110 and P is how many pitches he is alloted

Five friends decided to get together to bake cookies for a fundraiser. In total, they baked 144 cookies and packaged them in dozens. How many packages of cookies did they bake?

Answers

All you have to do is 144/12=12 so therefore there are 12 packages of cookies they had to bake for a fundraiser.

.........................................................I am d u m b

Write a polynomial function of least degree with real coefficients in standard form that has the given zeros. –2, –4, –3 + 4i

Answers

Given:

Zeroes of a polynomial are –2, –4, –3 + 4i.

To find:

The polynomial function of least degree with real coefficients in standard form.

Solution:

According to the complex conjugate root theorem, if a complex number a+ib is a zero of a polynomial, then its conjugate a-ib is also a zero of than polynomial.

–3 + 4i is zero of the polynomial. So, by complex conjugate root theorem -3-4i is also a zero of required polynomial.

If c is a zero of p(x), then (x-c) is a factor of p(x).

–2, –4, –3 + 4i, -3-4i are zeroes of the polynomials. So, (x+2), (x+4), (x+3-4i), (x+3+4i) are the factors of the required polynomial.

Let the required polynomial be p(x), so

[tex]p(x)=(x+2)(x+4)(x+3-4i)(x+3+4i)[/tex]

[tex]p(x)=(x^2+4x+2x+8)((x+3)^2-(4i)^2)[/tex]    [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]p(x)=(x^2+6x+8)(x^2+6x+9-16i^2)[/tex]    [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]p(x)=(x^2+6x+8)(x^2+6x+9-16(-1))[/tex]    [tex][\because i^2=-1][/tex]

[tex]p(x)=(x^2+6x+8)(x^2+6x+9+16)[/tex]

[tex]p(x)=(x^2+6x+8)(x^2+6x+25)[/tex]

[tex]p(x)=x^2(x^2+6x+25)+6x(x^2+6x+25)+8(x^2+6x+25)[/tex]

[tex]p(x)=x^4+6x^3+25x^2+6x^3+36x^2+150x+8x^2+48x+200[/tex]

Combining like terms, we get

[tex]p(x)=x^4+(6x^3+6x^3)+(25x^2+36x^2+8x^2)+(150x+48x)+200[/tex]

[tex]p(x)=x^4+12x^3+69x^2+198x+200[/tex]

Therefore, the required polynomial is [tex]p(x)=x^4+12x^3+69x^2+198x+200[/tex].

I dont understand this can someone plz explain.
the answer is A but how is it A?

Answers

Answer:

Step-by-step explanation:

here is what I think logically is going on.. and does this happen to be some kind of computer sciency class question?  b/c this seems like a primer for Boolean logic.. ask your teacher that question  :D  .. see if he knows :P anyway.. soooo  by subtracting 4 reds.....

R R B B B  our starting chips ( the letters represents the the chips below)

OOOOO    subtracting one red changes the next black to a red.. I think

R R R B B   (-1)

OOOOO subtract one more red changes the next black to a red

R R R R B   (-2)

OOOOO  subtract one more red

R R R R R  (-3)

OOOOO subtract one more and they all fip ..

B B B B B (-4)

OOOOO

This is a bit like a binary counter.. :/ why are you learning this :D

What type of lines are coplanar and do not intersect?
A) Parallel
B) Perpendicular
C) Segments
D) Transversal

Answers

Answer:

A(parallel

I hope this helps you

On a trip last summer, I used 20 gallons of gas to travel 600 miles. At this rate, how much gas
would I need to go 1500 miles?

Answers

Answer:

45,000

Step-by-step explanation:

You should divide 20 by 600 to see how many miles he would run per mile

and you take 30 x 1,500 to get your answer

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